Theorem REF  guarantees that (A) holds for any sequence of random vectors \(\mathbf {x}_p \)  following the random tensor model with \(p=\binom{n}{d}\)  and \(X_\alpha =X_\alpha (d,n)\) , when \(K_nd^2=o(n)\)  and \(n\rightarrow \infty \)  (here \(d, n \)  may depend on some parameter \(N\)  that goes to infinity). This along with Theorem REF  gives a version of the Marchenko-Pastur theorem for the random tensor model under the fourth moment condition, extending Theorem 1.5 of [1]}, where it is assumed that \(d^3=o(n)\)  and \(K_n=O(1)\) . We can state a more general result, assuming only that the second moments are finite.
